Gel polish is not beathable

All gel polish and soak-off gels are permeable. This means that they allow some liquids and gases to pass through the material. And of course, this is necessary otherwise soak-off liquid could not be absorbed and would not be effective. 

Permeability is the reason why some nail products are soak-off and others that are impermeable, are only file off. And if a material has microscopic holes in it to allow the transfer of thin liquids, then those holes will be big enough to also pass gases, including air and oxygen. 

But does the nail bed need to receive oxygen from the air through the nail plate? The answer to this is no, because the nail bed and the nail matrix receives oxygen and nutrients from the blood supply.